Question
When we heat an object, it expands. Is work done by the object in this process ? Is heat given to the object equal to the increase in its internal energy?

Answer

When we heat an object, it expands, i.e. its volume increases.
Work done by the system, $\Delta\text{W}=\text{P}\Delta\text{V}$
Using the first law of thermodynamics, we get,
$\Delta\text{Q}=\Delta\text{U}+\Delta\text{W}$
Since the volume changes, $\Delta\text{W}$ has some non-zero positive value. Thus, heat given to the object is not equal to the increase in the internal energy of the system.

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